Physics quiz question: Spire of Dubin pendulum length

Physics 205A Quiz 6, fall semester 2016
Cuesta College, San Luis Obispo, CA

"Jim Larkin Statue and the Spire of Dublin"
Tony Webster
flic.kr/p/kDoeVG

The Spire of Dublin is a monument containing internal pendulum systems to dampen vibrations. Its upper pendulum has a period of 3.6 s, and has a cable that suspends a 1,250 kg mass.[*][**][***] Neglect the mass of the cables. The upper pendulum has a cable length of:
(A) 1.8 m.
(B) 3.2 m.
(C) 3.8 m.
(D) 18 m.

[*] wki.pe/Spire_of_Dublin.
[**] sta.ie/perch/resources/lessons/a4dcclessoned.2.pdf.
[***] Matthew Wells, Skyscrapers: Structure and Design, Laurence King Publishing (2005), pp. 56-57.

Correct answer (highlight to unhide): (B)

The period of a pendulum is given by:

T = 2·π·√(L/g),

which does not depend on the mass. Since the period T = 3.6 s and gravitational constant g = 9.80 m/s² are known, the length L can then be solved for:

L = g·(T/(2·π))²,

L = (9.80 m/s²)·((3.6 s)/(2·π))² = 3.217150223 m,

or to two significant figures, the length of the pendulum cable is 3.2 m.

(Response (A) is (1/(2·π))·√(m/g); response (C) is 2·π·√(T/g); response (D) is (1/(2·π))·√(m·g).)

Sections 70854, 70855, 73320
Exam code: quiz06rn3T
(A) : 2 students
(B) : 51 students
(C) : 2 students
(D) : 0 students

Success level: 93%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.36